Question

When is a rhombus a rectangle

Answer 1

The dual polygon of a rhombus is a rectangle: A rhombus has all sides equal, while a rectangle has all angles equal.

Answer 2

A rhombus is a rectangle when it has four right angles (or when it is a square).

Explanation:

We need to remember that:

• A parallelogram is a quadrilateral with two pairs of parallel sides.
• A rhombus is a parallelogram with four equal sides.
• A rectangle is a parallelogram with four right angles.
• A square is a rectangle with four equal sides.

If we redefine a square like a parallelogram with four equal sides (rhombus) and parallelogram with four right angles (rectangle), then a square is a rectangle and a rhombus at the same time.

We know that if A = C and B = C, then A = B.

We can apply this to the next statements:

• A rhombus with four right angles is a square.
• A rectangle with four equal sides is a square.

• Then, a rhombus with four right angles = a rectangle with four equal sides = square.

Or, a rhombus with four right angles is a rectangle with four equal sides.

Then, a rhombus is a rectangle when it has four right angles, or when it is the same as a square.

Conclusion

A rhombus whose internal angles are all right angles is a rectangle with four equal sides, or a square.